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Presented at the 2003 Int. Symp. on Space THz Tech., Tucson, AZ, April 2003
ALMA Memo No. 467
29 May 2003
Measurements and Simulations of Overmoded Waveguide Components
at 70-118 GHz, 220-330 GHz and 610-720 GHz
G. A. Ediss
National Radio Astronomy Observatory
Charlottesville, VA 22903
Keywords: waveguide, waveguide transitions, waveguide components, loss measurement
Abstract
For low-loss transmission of the LO in the ALMA Band 6 cartridges, overmoded waveguide may be used.
In this paper, we report on the theoretical and measured losses of various sizes of waveguide in the
frequency ranges 70-118 GHz, 220-330 GHz and 610-720 GHz.
Introduction
The use of overmoded waveguide for low-loss transmission dates back to the earliest usage of waveguide
[1], [2], [3], [4]. This use is now quite standard in circular waveguide [5], [6] and in rectangular
waveguide [7], [8], [9], [10], [11]. In this paper, we deal with the transmission of the fundamental mode
(TE10) in overmoded rectangular waveguide. This mode is the easiest mode to generate and control in
signal sources and components such as couplers, hybrids, etc. as no mode converters are required. This
will be used for the transmission of the LO from the final multiplier in the Band 6 multiplier chain, which
will be on the 90 K or 20 K stage of the cartridge for thermal loading reasons, and the mixer, which will be
on the 4 K stage. Depending on the thermal load conditions, these two components will be up to 200 mm
apart. Due to waveguide losses and available/required power levels, losses should be as low as possible.
Theory
Loss, α, of the fundamental (TE10) mode is given by [12]
1/2 2
λ π λg b dB
α ( ( 1 ( 12 ( ( 8.676
b(λg λ (η (σ λc a m
where λ is the free space wavelength; λg is the waveguide wavelength in waveguide of width, a, and
height, b; σ is the conductivity of the wall material and η is the impedance of free space (120*π Ω). Figure
1 shows the theoretical loss for a frequency of 243 GHz as a function of waveguide width, a, for a/b = 2
(standard waveguide). The waveguide for Band 6 (WR3.7) is 0.94 x 0.47 mm (37 x 18.5 mils), for which
the loss would be approximately 18 dB/m for copper (σ = 4.00*107 S/m), and nearly 117 dB/m for stainless
steel (σ = 0.1*107 S/m), which is preferred for its thermal properties. These include the usual factor of 1.31
to account for surface roughness effects [13], and Tischer [13] also gives a further factor of 1.135** for an
“anomalous skin effect” in copper. Using WR10 (2.54 x 1.27 mm, 100 x 50 mils) as the overmoded
waveguide, the loss reduces to 3.8 dB/m and 26 dB/m, respectively.
Loss at fixed frequency (243 GHz)
40
Loss dB/meter
20
0
0 1000 2000
waveguide a (microns), a/b=2
Copper
Stainless Steel
Figure 1
Losses will, of course, be reduced by a factor of approximately 3 to 4 upon cooling copper to about 4 K
according to Wollack et al. [14], whereas for stainless steel the reduction is only about 25% [15].
Trapped Modes
One problem with using overmoded waveguide systems is the possibility of exciting unwanted modes that
can cause resonant losses [14], [16], [17], especially in systems where two tapers from/to fundamental
mode waveguide are used. The unwanted modes are reflected at some point in the tapers and are “trapped”
causing deep, narrow resonances. The frequency spacing, δf, can be very fine, depending upon the total
length between the reflection points, L [9]
λf λ
.
f 2L
The depth of the resonances is given by [10] as
(2(Pc(A)
1
Pmin 1 A
Pmax (2(Pc(A)
1
1 A
where Pmax is the power transmitted through the system away from resonance, Pc is the power converted
into the trapped mode (mode conversion), and A is the one-way power transmission of the trapped mode.
(Note that equation (2) given in [9] is incorrect.) Calculations are shown in Figure 2.
1
Losses in dB are multiplied by these factors.
M ode c onvers ion los s 35 dB
Depth of resonance dB
M ode c onvers ion los s 30 dB
10 M ode c onvers ion los s 25 dB
M ode c onvers ion los s 20 dB
M ode c onvers ion los s 15 dB
M ode c onvers ion los s 10 dB
5
0
0 .0 1 0 .1 1 10
One w a y tra ppe d m ode los s in dB
Figure 2
For typical tapers, the mode conversion is -20 dB (or better), with a one-way mode loss of 2 dB, and the
resonances are approximately 0.2 dB deep which is negligible. Cooling to 20 K, however, will reduce the
one-way loss to about 0.67 dB which will increase the resonance depth to 0.5 dB. Also of concern for
ALMA is any change in phase of the LO as it is tuned in frequency across a resonance. Unfortunately, it
has not been possible to measure the phase with any of the present measuring systems.
Trapped modes will also be excited by any bends or twists included in the waveguide between the tapers.
(H-plane bends are worse than E-plane bends in this regard for oversize waveguide with the usual E-field
orientation [9][10]. The opposite is true for “Tall” guide (reciprocal a to b ratio), but “Tall” guide has
more resonances.) Mode filters are difficult to use at these frequencies due to the small sizes and the large
number of modes (WR10 has 14 modes at 300 GHz, 62 at 700 GHz), all of which can be excited above
their cut-off frequencies by any discontinuities.
The width of the transmission resonances also gives an indication of the mode conversion level. [14] gives
the conversion as
π ∆f
Pc ( ( 1 Rmin
2 f
where Rmin is the depth of the resonance, f is the resonant frequency, and ∆f is the half-power width of the
resonance.
QuickWave and CST Calculations
QuickWave [18] or CST [19] Finite Difference Time Domain EM simulators can be used to analyze such
systems, but run into difficulty with such large structures (in wavelengths). As meshes with cell sizes of
less than approximately 0.1 wavelengths should be used [20], complete structures cannot be analyzed due
to memory limitations and calculation times. Partial structures can be analyzed (tapers, bends, etc.) which
give some idea of the problems. In runs with bends, trapped modes are clearly seen and the change in their
depth can be shown to be a function of material conductivity. QuickWave was used for the following.
Figure 3 shows the calculated transmission of a 12.7 mm linear taper from WR3.7 to WR10 with 2.54 mm
lengths of waveguide at each end, a 25.4 mm radius (center-line) 90-degree E-plane bend in WR10 and
then a similar taper with waveguide sections back to WR3.7 for a perfect conductor. Figure 4 is the same
geometry using a conductivity of 0.5*107 S/m (no surface roughness). Figures 5 and 6 show the phase for
these two cases, respectively, and show that there are phase effects for deep resonances. For small
resonances (< 1 dB), there are no phase effects. Similar effects can be achieved by inserting lossy material
in the waveguide to obtain the same one-way path loss, but this can add extra reflections at the front and
back surfaces of the material. Figure 7 shows the transmission and reflection of two lossless linear tapers
of 7.62 mm length, from WR3.7 to WR10, back-to-back with a section of overmoded waveguide, WR10,
of length 2.54 mm between them. Figure 7 also shows that tapers of sufficient length and perfect flange
alignment have very little mode conversion. Figure 8 shows the results for two 1.27 mm long lossless
tapers.
Figure 3. Calculated transmission (0-50 dB, 10 dB per division) as a function of
frequency (200-300 GHz, 20 GHz per division) of a 12.7 mm linear taper from
WR3.7 to WR10 with 2.54 mm lengths of waveguide at each end, a 25.4 mm radius
90 degree E-plane bend in WR10, and then a similar taper with waveguide sections
back down to WR3.7 for a perfect conductor.
Figure 4. Calculated transmission (0-50 dB, 10 dB per division) as a function of
frequency (200-300 GHz, 20 GHz per division) of a 12.7 mm linear taper from
WR3.7 to WR10 with 2.54 mm lengths of waveguide at each end, a 25.4 mm
radius 90-degree E-plane bend in WR10 and then a similar taper with waveguide
sections back down to WR3.7 for a conductivity of 0.5*107 S/m.
Figure 5. Transmission phase (+180 to –180 degrees) as a function of frequency
(200-300 GHz, 20 GHz per division) of a 12.7 mm linear taper from WR3.7 to
WR10 with 2.54 mm lengths of waveguide at each end, a 25.4 mm radius 90-
degree E-plane bend in WR10 and then a similar taper with waveguide sections
back down to WR3.7 for a perfect conductor.
Figure 6. Calculated transmission phase (+180 to –180 degrees) as a
function of frequency (200-300 GHz, 20 GHz per division) of a 12.7 mm
linear taper from WR3.7 to WR10 with 2.54 mm lengths of waveguide at
each end, a 25.4 mm radius 90-degree E-plane bend in WR10 and then a
similar taper with waveguide sections back down to WR3.7 for a
conductivity of 0.5*107 S/m.
Figure 7. S11 and S21 for two lossless WR3.5 to WR10 tapers (7.62 mm
long) back-to-back.
Figure 8. S11 and S21 for two lossless tapers WR3.5 to WR10 (1.27 mm long) back-
to-back.
Scale Model Measurements at 69-118 GHz (Scale factor 7.14 from Band 9, 600-700 GHz)
In vector network analyzer (VNA) measurements on a scale model, the distance between the VNA
(HP8510) heads is limited by the cable lengths to about 500 mm (equivalent to 70 mm at Band 9), and
mounting bends and twists to simulate the final waveguide run may not be possible. Figure 9 shows the
measured transmission of two tapers from WR10 to WR71.4, each 100 mm long placed back- to-back,
which clearly shows resonances (theoretical loss 0.18 dB for aluminum, roughness factor included). In the
scale model, aluminum was used for ease of manufacture, but the surface losses do not scale as required to
simulate the Band 6 waveguide (increasing as the square root of the frequency), so that the resonances are
much deeper than they would be in the final structure. The frequency scans were made with 801 points.
Figure 10 shows the transmission for two tapers 300 mm long (theoretical loss 0.52 dB for aluminum,
including roughness factor). Figure 11 shows the loss for a straight section of WR71.4 of length 190 mm
placed in between two tapers (divided by the transmission of the tapers alone). This figure has both
positive and negative resonances due to the shift in frequency of the resonances as the length is changed
and the subtraction of the taper loss. The loss of the straight section matches well with the theoretical,
including roughness factor (also shown in Figure 11).
I n se r tio n o f tw o W R 7 1 .4 (sc a l e d fr o m W R 1 . 4 - b a n d 9 )
1 0 0 m m ta p e rs b a c k to b a c k
0
-0 . 5
S21 dB
-1
-1 . 5
-2
70 80 90 100 110 120
F re q u e n cy G H z
Figure 9
In s e r tio n o f tw o W R 7 1 .4 (s c a le d fr o m W R 1 .4 -b a n d 9 )
3 0 0 m m lo n g ta p e r s b a c k to b a c k
0
-0 . 5
S21 dB
-1
-1 . 5
-2
70 80 90 100 110 120
F re q u e n cy G H z
Figure 10
In s e rtio n o f 1 9 0 m m le n g th o f W R 7 1 .4
(s c a le d fro m b a n d 9 )
0
-0 . 1
S21 dB
-0 . 2
-0 . 3
-0 . 4
-0 . 5
70 80 90 100 110 120
F re q u e n cy G H z
M e a s u re d Th e o re t ic a l fo r A lu m in u m
Figure 11
In s e r tio n o f 3 0 0 m m E -p la n e b e n d in W R 7 1 .4
(s c a le d fr o m b a n d 9 )
0
-2
S21 dB
-4
-6
-8
-1 0
70 80 90 100 110 120
F re q u e n c y G H z
Figure 12
Figure 12 gives the insertion of a 300 mm long, (center-line) 90-degree, E-plane bend. Figure 13 gives the
insertion of a 300 mm long (center-line), 90-degree, H-plane bend. (In both figures, the transmission of
the tapers is subtracted.)
In s e rtio n o f 3 0 0 m m H -p la n e b e n d in W R 7 1 .4
(s c a le d fro m b a n d 9 )
0
-5
S21 dB
-1 0
-1 5
-2 0
70 80 90 100 110 120
F re q u e n c y G H z
Figure 13
Measurements at 624-720 GHz with WR10 Components
Measurements at 624-720 GHz were made using a x6-multiplied Gunn (RPG [21]) and an overmoded
power head (Anritsu 90-140 GHz [22]). The frequency was set by hand with no phase lock, and power
levels were measured with and without the device under test between two WR3.4 to WR10 tapers (back-to-
back). Figure 14 shows the measured and theoretical losses for a 152.4-mm length of WR10 stainless steel
waveguide, and for the same waveguide after plating with 2.5 microns of copper. (12 mm at each end was
copper-plated on the inside during attachment of the waveguide flanges; this is accounted for in the
theoretical values.) The theoretical values include the 1.3 roughness factor for both, and the 1.135 skin-
effect factor for copper but not for stainless steel [13]. There was insufficient power near 700 GHz to
make any measurements.
Losses
0
-1
152.4mm Stainless steel w aveguide WR10
-2 152.4mm WR10 guide Cu plated
152.4mm copper theory WR10
dB
-3 152.4mm Stainless steel theory WR10
-4
-5
-6
620 640 660 680 700 720
Frequency GHz
Figure 14
This clearly shows the improvement of plating copper or gold on the inside of the waveguide, but for very
small waveguide (WR8 or smaller) or long lengths (100 mm or longer) this is extremely difficult. The
sample was also measured at 75-110 GHz where it had 3.26-2.25 dB, unplated (compared to theoretical
values, with roughness factor, and accounting for copper-plated sections at the ends, of 4.4 - 3.1 dB) and
0.63-0.47 dB, plated ( theoretical values 0.76-0.54 dB with skin effect and roughness factors). The
difference with the theoretical values can be explained if the waveguide is slightly larger than the nominal
2.54 by 1.27 mm. The losses of various components (H-plane bend {Aerowave [23]}, H-plane bend, E-
plane bend and 90-twist {Baytron [24]}) are given in Figure 15. The reason for the difference between the
two H-bends is unknown.
Losses
0
-2
-4
dB
-6
-8
-1 0
620 640 6 60 6 80 70 0 72 0
H b e nd B ay t ro n
F re q u e n cy G H z H b e nd A ero w a ve
E b e nd
Tw is t
Figure 15
Two sections of WR1.4 (fundamental waveguide for this band) were made of brass in split-block technique
and then gold-plated. One piece, 25.4 mm long, split in the narrow wall (incorrect wall) and one piece,
76.2 mm long, split in the broad wall. They had losses of 389 dB/m and 130 dB/m, respectively, at 684
GHz (theoretical value 130 dB/m with roughness factor).
Measurements at 220-330 GHz with WR10 Components
Measurements have been made in the range 220-330 GHz (0.5 GHz per point) using an HP8510 with WR3
extender heads (Oleson [25]). Again, spacing between the heads limits the size of structures which can be
measured. Also, the system sensitivity and dynamic range are limited at these frequencies. Figure 16
shows the measured transmission of a taper from WR3.4 to WR10, 200 mm of waveguide followed by two
H-plane bends and then one E-plane bend (all WR10 [24]) and then a taper from WR10 to WR3.4, divided
by the system response with the heads connected directly together2. This shows that at room temperature
there are no major resonances. Note that the fluctuations below 220 GHz and above 300 GHz are due to
the low power levels in these frequency ranges. No resonances were seen when the frequency range was
reduced to 240-245 GHz (0.025 GHz per point). Also shown in Figure 16 is the measured loss of two
tapers, back-to-back, which have a theoretical loss of 0.38 dB for copper, including roughness and skin-
effect factors.
It was not possible to cool the waveguide run to determine if resonances become significant when cold.
Figure 17 shows the insertion loss of 150 mm of WR10, copper-plated, and stainless steel WR6 and WR5,
measured between two tapers, over the frequency range 220-330 GHz, and compares it to the theoretical
values (with roughness factors and skin-effect factors for copper-plated WR10) for those waveguides.
2
Full VNA calibration was not available on this instrument at the time it was used.
In s e rtio n o f W R 1 0 c o m p o n e n ts .
2 Ta p e rs
4 2 Ta p e rs t h e o re t ic a l
2 2 0 0 m m le n g t h , 2 H -p la n e a n d 1 E -p la n e
Insertion dB
0
-2
-4
-6
-8
-1 0
211 231 251 271 291 311 331
F re q u e n c y G H z
Figure 16.
In s e r tio n o f 1 5 0 m m o f o v e r m o d e d w a v e g u id e
0
-2 W R 1 0 m e a s u re d
Insertion dB
-4 W R 1 0 t h e o ry
-6 W R 6 m e a s u re d
-8 W R 6 t h e o ry
-1 0 W R 5 m e a s u re d
-1 2 W R 5 t h e o ry
220 270 320
F re q u e n cy G Hz
Figure 17. WR10 is copper-plated; WR6 and WR5 are stainless steel.
The excess loss of the WR10 is probably due to difficulties in plating, as measurements at
75-100 GHz show that this waveguide has twice the loss we usually measure for copper-plated stainless
steel WR10.
Measurements of overmoded waveguide (WR10) made at IRAM for Band 7 at room temperature also
show no resonances [26].
Conclusions
Overmoded waveguide is a possibility for low-loss LO transmission at Band 6, but trapped modes may be a
problem when operated at cryogenic temperatures. Measured loss of straight waveguide compares well
with theory when roughness and skin-effect loss factors are included. A simulation (at room temperature)
of a 25.4-mm taper from WR3.4 to WR10, 150 mm of WR10 followed by a 25.4-mm taper back to WR3.4,
had 1.0 dB loss with 0.3 dB resonances (20 dB mode coupling assumed), i.e., maximum depth 1.3 dB, for
copper (with roughness and skin-effect factors included), and 4.4 dB loss with 0.1 dB resonances if the
WR10 section is unplated stainless steel (including roughness factor). To reduce phase problems, stainless
steel may need to be used if the extra loss can be tolerated. Losses will reduce by approximately a factor of
two when cooled to 90 K for copper, but the resonances will deepen (to approximately 0.6 dB loss with 2
dB resonances). Losses will reduce to 3.3 dB with 0.2 dB resonances for stainless steel.
Acknowledgment
I would like to thank Dr. J. Hesler (UVA) for allowing me to use the HP8510 with WR3 heads.
References
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(1976), pp. 853-858.
[14] E. J. Wollack, W. Grammar and J. Kingsley, “The Bφifot orthomode junction.” ALMA Memo 425.
http://www.alma.nrao.edu/memos/html-memos/abstracts/abs425.html
[15] S. Weinreb, “Cryogenic performance of microwave terminations, attenuators, absorbers and coaxial
cable,” NRAO Electronics Division Internal Report No. 223, January 1982.
[16] A. P. King and E. A. Marcatili, “Transmission loss due to resonance of loosely-coupled modes in a
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[18] QuickWave FDTD EM simulator, QWED s.c. Zwyciezcow 34/2, 03-938 Warszawa, Poland.
http://www.qwed.com.pl/
[19] CST Microwave Studio, Sonnet Software, Inc., 1020 Seventh North St., Suite 210,
Liverpool, NY 13088. Phone: 315-453-3096, fax: 315-451-1694.
http://www.sonnetusa.com/index.asp
[20] W. Gwarek (QuickWave), private communication.
[21] RPG Radiometer Physics GmbH, Birkenmaarstr. 10, D-53340 Meckenheim, Germany.
Tel: (49) 02225-999810, radiometer.physics@t-online.de
[22] Anritsu ML83A with MP82B head. http://www.anritsu.com
[23] Aerowave, Inc., 344 Salem St., Medford, MA 02155. Phone: (781) 391-5338.
[24] Baytron (now Aerowave). See [23].
[25] Oleson Microwave Laboratories, 355 Woodview Dr., Suite 300, Morgan Hill, CA 95037. Phone:
(408) 779-2698, fax: (408) 778-0491. http://www.oml-mmw.com/
[26] S. Claude. (IRAM), private communication.
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